Cremona's table of elliptic curves

198 = 2 · 3² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11-	Signs for the Atkin-Lehner involutions
Class	198d	Isogeny class
Conductor	198	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	574992 = 24 · 33 · 113	Discriminant
Eigenvalues	2+ 3+  0  2 11-  2  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-87,333]	[a1,a2,a3,a4,a6]
j	2714704875/21296	j-invariant
L	0.97436372977461	L(r)(E,1)/r!
Ω	2.9230911893238	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	1584h1 6336b1 198c3 4950z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198d1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	+	0	2	-	2	6	2	0	6	-4	2	-6	-10	-12	12	-12	-10	8	-12	14	2	12	0	2

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Quadratic twists for elliptic curve 198d1

-4	8	-3	5	-7	-11	13	17	-19	-23
1584h1	6336b1	198c3	4950z1	9702i1	2178g1	33462bp1	57222a1	71478bn1	104742a1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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